How can I stop the 'bloom' effect shifting direction in eevee?
Thank you for the help, none of the solutions fixed what I needed unfortunately.
However I did manage to fix the problem, and for anyone who is facing a similar issue, here's how I did it.
I figured out that the way bloom was being calculated was in relation to the emitters angle to the camera. With my shake being set on the x axis, small rotations were being amplified by the bloom effect because the angle in relation to the camera was changing and as a result, so was the direction it was 'blooming' the light.
To fix it, I made one very simple change, instead of a shake in the rotation, I applied the effect to the translation in the z axis. The motion feels pretty much exactly the same, but instead of it changing the angle the camera points at, it moves the whole camera up and down a bit. It's worth pointing out there will still be some shift in the bloom effect as the translation still adjusts the angle a bit, but its a lot less noticeable now.
Mission accomplished!